Hi there!
From your itinerary it looks like you'll be in Japan for 13 days. Before looking at which rail pass makes sense for you, lets take at the costs for the travel you list:
- Narita airport terminal 1 > Shinjuku(jr): ¥3110, (88mins, 89km)
- Shinjuku(jr) > Nikko: ¥4820, (113mins, 147km)
- Nikko > Shinjuku(jr): ¥4820, (137mins, 147km)
- Shinjuku(jr) > Kamakura: ¥890, (61mins, 57km)
- Kamakura > Shinjuku(jr): ¥890, (69mins, 57km)
- Shinjuku(jr) > Maihama: ¥380, (47mins, 23km)
- Maihama > Shinjuku(jr): ¥380, (48mins, 23km)
- Shinjuku(jr) > Kyoto: ¥13220, (185mins, 517km)
- Kyoto > Odawara: ¥11750, (181mins, 429km)
- Odawara > Tokyo: ¥1450, (36mins, 83km)
- Tokyo > Narita airport terminal 1: ¥2940, (58mins, 79km)
TOTAL: ¥44650 for 11 legs
I have excluded other exploration around Tokyo - while you can use the Japan Rail Pass to use the JR system in Tokyo (maps) you may also choose to use the Metro system which is not JR.
For Hakone, from Odawara you will need to use the Odakyu Hakone Railway system to get up to Hakone as it is not a JR operated line. You can find out more on the Hakone free pass online.
As the 14 day rail pass is ¥45,100 there is not much difference in purchasing this over separate tickets aside from convenience and the freedom to perhaps expand on what you have listed with some other trips.
If you are pretty decided on your itinerary, how about the following itinerary that uses a 7 day rail pass:
Purchase a combined return [Narita Express (N'EX) + Suica] card deal on arrival at Narita going to Shinjuku. This will cost ¥5500 and include both return ticket on the Narita express, and ¥2000 value pre-paid 'suica' travel card making a saving of ¥2720 over buying these separately. You will then be able to use the Suica card to travel around Tokyo on either the JR or Metro services.
Purchase a separate return to Kamakura/Disney or use the Suica card.
Activate a 7 day japan rail pass on the 14th, aiming to use it until the 20th to travel to Nikko, Kyoto, Odawara (for Hakone) and back to Tokyo on the 20th
At Odawara purchase the Hakone free pass to travel up to Hakone.
This will bring your total spend to:
- ¥5500: N'EX + Suica
- ¥1000: Extra travel in Tokyo
- ¥28300: 7 day Japan Rail Pass
- ¥3900: Hakone free pass
TOTAL: 38,700 (including all travel inside Tokyo and up to Hakone)
With this option you will make a saving of ¥10,300 over a 14 day pass + Hakone free pass, or a saving of ¥9850 over separate tickets.
Aside from price, the main difference between these options is in terms of flexibility. As the 7 day option I outline above will still leave you with some flexibility (during the rail pass period) along with offering the most saving, I recommend this approach.
Hope this helps!